Bend loss resistant multi-mode fiber

ABSTRACT

A graded index multimode optical fiber comprising: (a) a silica core doped with germania, and at least one co-dopant, comprising one of P 2 O 5  or F or B 2 O 3 , the core extending to outermost core radius, r 1  and having a dual alpha, α 1 ; (b) a low index inner cladding surrounding the core and off-set from said core; (c) an outer cladding surrounding and in contact with the inner cladding, such that at least the region of the inner cladding off-set from said core has a lower refractive index than the outer cladding. The center germania concentration at the centerline, C Ge1 , is greater than or equal to 0, and an outermost germania concentration in the core C Ge2 , at r 1  is greater than or equal to 0. The core has a center co-dopant concentration at the centerline, C c-d1 , greater than or equal to 0, and an outermost co-dopant concentration C c-d2 , at r 1 , wherein C c-d2  is greater than or equal to 0.

BACKGROUND

The disclosure relates generally to optical fibers, and particularly tograded index multimode fibers, and more particularly to graded indexgermania multimode fibers that have graded index cores codoped with Geand another dopant and that exhibit low bend losses.

SUMMARY

Some embodiments of the disclosure relate to optical fibers withgermania (GeO₂) and another dopant in the core of the fiber.

According to at least one embodiment a graded index multimode opticalfiber comprises:

-   -   (a) a core comprising silica doped with germania and at least        one co-dopant, c-d, the co-dopant comprising one of P₂O₅ or F or        B₂O₃, the core extending from a centerline at r=0 to an        outermost core radius, r₁ and having a dual alpha, α₁ and α;    -   (b) an inner cladding surrounding and in contact with the core;    -   (c) an outer cladding surrounding and in contact with the inner        cladding, at least a portion of the inner cladding having a        lower refractive index than the outer cladding; and    -   the germania is disposed in the core with a germania dopant        concentration profile, C_(Ge1)(r), and the core has a center        germania concentration at the centerline, C_(Ge1), greater than        or equal to 0, and an outermost germania concentration C_(Ge2),        at r₁, wherein C_(Ge2), is greater than or equal to 0; and    -   wherein the co-dopant is disposed in the core with a co-dopant        concentration profile, C_(c-d)(r), and the core has a center        co-dopant concentration at the centerline, C_(c-d1), greater        than or equal to 0, and an outermost co-dopant concentration        C_(c-d2), at r₁, wherein C_(c-d2) is greater than or equal to 0;        and    -   C_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);    -   C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;    -   1.8≦₁≦2.4, 1.8≦αa₂≦3.1; and −10≦x₁≦10 and −10≦x₂≦10.

According to some embodiments a graded index multimode optical fibercomprises:

a core comprising silica doped with germania and at least one co-dopant,c-d, the co-dopant comprising one of P₂O₅ or F or B₂O₃, the coreextending from a centerline at r=0 to an outermost core radius, r₁ andhaving a dual alpha, α₁ and α;

-   -   (b) an inner cladding surrounding and in contact with the core;    -   (c) an outer cladding surrounding and in contact with the inner        cladding, at least one region of the inner cladding having a        lower refractive index than the outer cladding and being off-set        from said core; and    -   the germania is disposed in the core with a germania dopant        concentration profile, C_(Ge1)(r), and the core has a center        germania concentration at the centerline, C_(Ge1), greater than        or equal to 0, and an outermost germania concentration C_(Ge2),        at r₁, wherein C_(Ge2), is greater than or equal to 0; and    -   wherein the co-dopant is disposed in the core with a co-dopant        concentration profile, C_(c-d)(r), and the core has a center        co-dopant concentration at the centerline, C_(c-d1), greater        than or equal to 0, and an outermost co-dopant concentration        C_(c-d2), at r₁, wherein C_(c-d2) is greater than or equal to 0;        and    -   C_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);    -   C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;    -   1.8<₁<2.4, 1.8<α₂<3.1; and −10<x₁<10 and −10<x₂<10.

According to some embodiments the graded index multimode optical fibercomprises:

a core comprising silica doped with germania and at least one co-dopant,c-d, the co-dopant comprising B₂O₃, the core extending from a centerlineat r=0 to an outermost core radius, r₁ and having a dual alpha, α₁ andα;

-   -   (b) an inner cladding surrounding and in contact with the core;    -   (c) an outer cladding surrounding and in contact with the inner        cladding, at least one region of the inner cladding having a        lower refractive index than the outer cladding; and    -   the germania is disposed in the core with a germania dopant        concentration profile, C_(Ge1)(r), and the core has a center        germania concentration at the centerline, C_(Ge1), greater than        or equal to 0, and an outermost germania concentration C_(Ge2),        at r₁, wherein C_(Ge2), is greater than or equal to 0; and    -   wherein the co-dopant is disposed in the core with a co-dopant        concentration profile, C_(c-d)(r), and the core has a center        co-dopant concentration at the centerline, C_(c-d1), greater        than or equal to 0, and an outermost co-dopant concentration        C_(c-d2), at r₁, wherein C_(c-d2) is greater than or equal to 0;        and    -   C_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);    -   C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;    -   1.8<₁<2.4, 1.8<α₂<3.1; and 31 10<x₁<10 and −10<x₂<10.

Preferably, the silica based cladding region surrounding the core hasrefractive index lower than that of pure silica. In some embodimentsthis silica based region is down-doped with F and/or B and mayoptionally include Ge. In some embodiments, this silica based claddingregion includes random or non-periodically distributed voids (forexample filled with gas).

In some embodiments the core comprises about 200 to 2000 ppm by wt. Cl,and less than 1.2 wt. % of other index modifying dopants.

Preferably, the fiber has a numerical aperture NA between about 0.185and 0.25 (e.g., 0.185≦NA≦0.23, or 0.185≦NA≦0.215, or 0.195≦NA≦0.225, or2≦NA≦2.1) and a bandwidth greater than 2 GHz-Km at a at least onewavelength within 800 nm and 900 nm.

According to one embodiment a gradient index multimode fiber comprises:(i) a silica based core (with at least one core region) co-doped withGeO₂ and about 1 to 9 mole % P₂O₅, and about 200 to 2000 ppm by wt. Cl,and less than 1 wt. % of other index modifying dopants; the core havinga dual alpha, α₁ and α₂, where 1.8≦α₁≦2.25 and 1.9≦α₂≦2.25 at least onewavelength in the wavelength range between 840 and 1100 nm, preferablyat 850 nm; and (ii) a silica based region surrounding the core regioncomprising F and optionally GeO₂ and having a refractive index lowerthan that of silica. The fiber has a numerical aperture between 0.185and 0.215.

According to some embodiments the multimode fiber comprises: (i) asilica based core co-doped with GeO₂ and about 0.5 to 10 mole % P₂O₅(and preferably 1 to 8 mole %), and less than 1 wt. % of other indexmodifying dopants; the core having a dual alpha, α₁ and α₂, where1.8≦α₁≦3.4 and 1.9≦α₂≦2.4 at least one wavelength in the wavelengthrange between 840 and 1100 nm, (preferably at 850 nm) and a physicalcore diameter, Dc where Dc=2R₁ and wherein 25≦Dc≦55 microns, and in someembodiments 25≦Dc≦45 microns; and (ii) a silica based cladding regionthat (a) surrounds the core and comprises F and optionally GeO₂ and (b)has a refractive index lower than that of silica. The fiber 10 has anumerical aperture between 0.185 and 0.215; a bandwidth greater than 2GHz-Km at least one wavelength situated in a range of 800 and 900 nm.

According to some embodiments the multimode fiber comprises: (i) asilica based core co-doped with GeO₂ and about 0.5 to 10 mole % P₂O₅(and preferably 1 to 8 mole %), and less than 1 wt. % of other indexmodifying dopants; the core having a dual alpha, α₁ and α₂, where1.8≦α₁≦2.4 and 1.9≦α₂≦2.4 at least one wavelength in the wavelengthrange between 840 and 1100 nm, (preferably at 850 nm) and a physicalcore diameter, Dc where Dc=2R₁ and wherein 45≦Dc≦55 microns; and (ii) asilica based cladding region that (a) surrounds the core and comprises Fand optionally GeO₂ and (b) has a refractive index lower than that ofsilica. The fiber 10 has a numerical aperture between 0.185 and 0.215; abandwidth greater than 2 GHz-Km at least one wavelength situated in arange of 800 and 900 nm.

According to some embodiments the multimode fiber The fiber 10 has anumerical aperture between 0.185 and 0.25 (e.g., 0.195≦NA≦2.25); abandwidth greater than 2 GHz-Km at least one wavelength situated in arange of 800 nm and 900 nm and a bandwidth greater than 2 GHz-Km atleast one wavelength situated in a range of 900 nm and 1300 nm.

According to at least some embodiments the multimode fiber has a gradedindex core and provides a bandwidth characterized by a first peakwavelength λp₁ situated in a range 800 and 900 nm and a second peakwavelength λp₂ situated in a wavelength range of 950 to 1700 nm.According to some embodiments the multimode fiber provides a bandwidthcharacterized by λp₁ situated in a range 800 nm and 900 nm and λp₂situated in a range of 950 to 1670 nm.

According to some embodiments the multimode fiber has a graded indexcore. Each of the dual dopants, germania and the codopant, are disposedin the core of the multimode fiber in concentrations which vary withradius and which are defined by two alpha parameters, α₁ and α₂. Thatis, the germania dopant concentration varies with radius as a functionof the alpha parameters, α₁ and α₂, as does the co-dopants dopantconcentration. The dual dopant concentrations disclosed herein alsoreduce the sensitivity with wavelength of the overall α shape of therefractive index of the optical fiber, which can help increase theproductivity yield of such fibers during their manufacture, therebyreducing waste and costs. As used herein, the term graded index refersto a multimode optical fiber with a refractive index having an overalldual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4 at least onewavelength in the wavelength range between 840 and 1100 nm, preferablyat 850 nm.

In some embodiments, the MMF disclosed herein comprises a refractiveindex profile which provides an RMS pulse broadening of less than 0.2ns/km (less than about 2 GHz-km) over wavelength window width of atleast 0.04 μm, preferably at least 0.05 μm, more preferably at least0.10 μm, and even more preferably at least 0.15 μm, wherein the windowis centered at about 0.85 μm. In some embodiments, an RMS pulsebroadening of less than 0.2 ns/km is provided over a wavelength windowwidth of at least 0.20 μm, and the window is preferably centered at awavelength in the 0.8 to 0.9 μm range (e.g., at about 0.85 μm).

In some embodiments, the MMF disclosed herein comprises a refractiveindex profile which provides an RMS pulse broadening of less than 0.02ns/km over wavelength window width of at least 0.04 μm, preferably atleast 0.05 μm, more preferably at least 0.10 μm, and even morepreferably at least 0.15 μm, wherein the window is centered at about0.85 μm. In some embodiments, an RMS pulse broadening of less than 0.02ns/km is provided over a wavelength window width of at least 0.20 μm,and the window is preferably centered at a wavelength in the 0.8 to 0.9μm range (e.g., at about 0.85 μm).

In some embodiments, the MMF disclosed herein comprises a refractiveindex profile which provides a bandwidth greater than 2 GHz-Km overwavelength window width of at least 0.04 μm, preferably at least 0.05μm, more preferably at least 0.10 μm, and even more preferably at least0.15 μm, wherein the window is centered at about 0.85 μm. In someembodiments, an RMS pulse broadening of less than 0.2 ns/km is providedover a wavelength window width of at least 0.20 μm, and the window ispreferably centered at a wavelength in the 0.8 to 0.9 μm range (e.g., atabout 0.85 μm). In these embodiments the core preferably has a gradedindex profile.

In some embodiments, the MMF disclosed herein comprises a refractiveindex profile which provides a bandwidth greater than 4 GHz-Km overwavelength window width of at least 0.04 μm, preferably at least 0.05μm, more preferably at least 0.10 μm, and even more preferably at least0.15 μm, wherein the window is centered at about 0.85 μm. In someembodiments, an RMS pulse broadening of less than 0.2 ns/km is providedover a wavelength window width of at least 0.20 μm, and the window ispreferably centered at a wavelength in the 0.8 to 0.9 μm range (e.g., atabout 0.85 μm). In these embodiments the core preferably has a gradedindex profile.

In some embodiments, the MMF disclosed herein comprises a refractiveindex profile which provides a bandwidth greater than 2 GHz-Km at 0.85μm, and a bandwidth greater than 0.75 GHz-Km at 0.98 μm. In someembodiments, the MMF disclosed herein comprises a refractive indexprofile which provides a bandwidth greater than 2 GHz-Km at 0.85 μm, anda bandwidth greater than 1.5 GHz-Km at 0.98 μm. In some embodiments, theMMF disclosed herein comprises a refractive index profile which providesa bandwidth greater than 2 GHz-Km at 0.85 μm, and a bandwidth greaterthan 2 GHz-Km at 0.98 μm. In some embodiments, the MMF disclosed hereincomprises a refractive index profile which provides a bandwidth greaterthan 2 GHz-Km at 0.85 μm, and a bandwidth greater than 0.75 GHz-Km at1.3 μm. In some embodiments, the MMF disclosed herein comprises arefractive index profile which provides a bandwidth greater than 2GHz-Km at 0.85 μm, and a bandwidth greater than 1 GHz-Km for at leastone wavelength between 0.98 and 1.66 μm. In some embodiments, the MMFdisclosed herein comprises a refractive index profile which provides abandwidth greater than 4 GHz-Km at 0.85 μm, and a bandwidth greater than1 GHz-Km for at least one wavelength between 0.98 and 1.66 μm. In theseembodiments the core preferably has a graded index profile.

In one set of embodiments, a first window is centered at about 0.85 μmand a second window is centered at a wavelength less than about 1.4 μm.In another set of embodiments, a first window is centered at about 0.85μm and a second window is centered at a wavelength less than about 1.56μm.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understand the natureand character of the claims.

The accompanying drawings are included to provide a furtherunderstanding, and are incorporated in and constitute a part of thisspecification. The drawings illustrate one or more embodiment(s), andtogether with the description serve to explain principles and operationof the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a cross-sectional view of oneembodiment of the optical fiber as disclosed herein;

FIG. 2A depicts a schematic refractive index profile of one embodimentof a graded index multimode fiber;

FIG. 2B depicts a schematic refractive index profile of anotherembodiment of a graded index multimode fiber;

FIG. 2C is a plot of dopant concentration C_(Ge) and C_(P) vs.normalized core radius, for one exemplary fiber corresponding to FIG.2A;

FIG. 3 schematically depicts the Ge dopant concentration profile in thecore of a comparative graded index multimode fiber with only germania inthe core;

FIG. 4 shows the root mean square (RMS) pulse broadening as a functionof wavelength for the fiber of FIG. 3A;

FIG. 5 shows the root mean square (RMS) pulse broadening as a functionof wavelength for several exemplary embodiments of Ge and P co-dopedfibers;

FIG. 6 illustrates the change in the second window center wavelength forsome embodiments of Ge and P co-doped fibers; and

FIG. 7 shows the root mean square (RMS) pulse broadening in ns/km at1310 nm vs. P doping level in the fiber core for several exemplaryembodiments of Ge and P co-doped fibers.

DETAILED DESCRIPTION

Additional features and advantages of the invention will be set forth inthe detailed description which follows and will be apparent to thoseskilled in the art from the description or recognized by practicing theinvention as described in the following description together with theclaims and appended drawings.

The “refractive index profile” is the relationship between refractiveindex or relative refractive index and waveguide fiber radius.

The “relative refractive index percent” is defined as Δ %=100×(n_(i)²−n_(c) ²)/2n_(i) ², where n_(i) is the maximum refractive index inregion i, unless otherwise specified, and n_(c) is the refractive indexof pure silica. As used herein, the relative refractive index isrepresented by Δ (and δ) and its values are given in units of “%”,unless otherwise specified. An “updopant” is herein considered to be adopant which has a propensity to raise the refractive index relative topure undoped SiO₂. A “downdopant” is herein considered to be a dopantwhich has a propensity to lower the refractive index relative to pureundoped SiO₂. One or more other dopants which are not updopants may bepresent in a region of an optical fiber having a positive relativerefractive index. A downdopant may be present in a region of an opticalfiber having a positive relative refractive index when accompanied byone or more other dopants which are not downdopants. The terms germania,Ge and GeO₂ are used interchangeably herein and refer to GeO₂. The termsphosphorus, P and P₂O₅ are used interchangeably herein and refer toP₂O₅. The terms boron, B and B₂O₃ are used interchangeably herein andrefer to B₂O₃

The optical core diameter is measured using the technique set forth inIEC 60793-1-20, titled “Measurement Methods and Test Procedures—FiberGeometry”, in particular using the reference test method outlined inAnnex C thereof titled “Method C: Near-field Light Distribution.” Tocalculate the optical core radius from the results using this method, a10-80 fit was applied per section C.4.2.2 to obtain the optical corediameter, which is then divided by 2 to obtain the optical core radius.

As used herein, numerical aperture (NA) of the fiber means numericalaperture as measured using the method set forth in TIA SP3-2839-URV2FOTP-177 IEC-60793-1-43 titled “Measurement Methods and TestProcedures-Numerical Aperture”.

Macrobend performance is determined according to FOTP-62(JEC-60793-1-47) by wrapping 1 turn around a 10 mm diameter mandrel andmeasuring the increase in attenuation due to the bending using anencircled flux (EF) launch condition (this is also referred to as arestricted launch condition). The encircled flux is measured bylaunching an overfilled pulse into an input end of a 2 m length ofInfiniCor® 50 micron core optical fiber which is deployed with a 1 wrapon a 25 mm diameter mandrel near the midpoint. The output end of theInfiniCor® 50 micron core optical fiber is spliced to the fiber undertest, and the measured bend loss is the difference of the attenuationunder the prescribed bend condition to the attenuation without the bend.The overfilled bandwidth is measured according to FOTP-204 using anoverfilled launch.

According to the following embodiments, the graded index multimodeoptical fiber includes a core comprising silica doped with germania andat least one co-dopant (c-d); an inner cladding surrounding and incontact with the core; and an outer cladding surrounding and in contactwith the inner cladding. The co-dopant (the second core dopant) isselected from at least one of the following materials: P₂O₅, F and/orB₂O₃. The core extends from a centerline at r=0 to an outermost coreradius, r₁ and has a dual alpha, α₁ and α. The germania is disposed inthe core with a germania dopant concentration profile, C_(Ge1)(r), andthe core has a center germania concentration at the centerline, C_(Ge1),greater than or equal to 0, and an outermost germania concentrationC_(Ge2), at r₁, wherein C_(Ge2), is greater than or equal to 0. Theco-dopant is disposed in the core with a co-dopant concentrationprofile, C_(c-d)(r), and the core has a center co-dopant concentrationat the centerline, C_(c-d1), greater than or equal to 0, and anoutermost co-dopant concentration C_(c-d2), at r₁, and (i) C_(c-d2) isgreater than or equal to 0; (b)C_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);(c)C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;(d) 1.8<₁<2.4, 1.8<α₂3.1; and wherein −10<x₁<10 and −10<x₂<10.

According to some embodiments wherein the inner cladding region includesrandom voids or is comprised of silica doped with boron, fluorine, orco-doping of fluorine and germania.

The voids (also referred as holes herein) can be non-periodicallydisposed in the depressed-index annular region 50. By “non-periodicallydisposed” or “non-periodic distribution”, we mean that when one takes across section (such as a cross section perpendicular to the longitudinalaxis) of the optical fiber, the non-periodically disposed holes arerandomly or non-periodically distributed across a portion of the fiber.Similar cross sections taken at different points along the length of thefiber will reveal different cross-sectional hole patterns, i.e., variouscross sections will have different hole patterns, wherein thedistributions of holes and sizes of holes do not match. That is, thevoids or holes are non-periodic, i.e., they are not periodicallydisposed within the fiber structure. These holes are stretched(elongated) along the length (i.e. parallel to the longitudinal axis) ofthe optical fiber, but do not extend the entire length of the entirefiber. While not wishing to be bound by theory, it is believed that theholes extend less than a few meters, and in many cases less than 1 meteralong the length of the fiber.

In some embodiments a maximum the voids in region 50 have a maximumdiameter of 15 microns; in other embodiments, at least 90% of theplurality of non-periodically disposed voids comprises a maximum averagehole diameter of 10 microns; in other embodiments, the plurality ofnon-periodically disposed holes comprises an average void diameter ofless than 2000 nm; in other embodiments, the depressed-index annularportion comprises a regional void area percent greater than 0.5 percent;in other embodiments, the depressed-index annular portion comprises aregional void area percent of between 1 and 20 percent; in otherembodiments, the depressed-index annular portion comprises a total voidarea percent greater than 0.05 percent.

As depicted in FIG. 1, the optical fiber 10 of the embodiments disclosedherein comprises a silica based core 20 and a silica based claddinglayer (or cladding) 200 surrounding and directly adjacent (i.e. incontact with) the core. Preferably, the fiber has a numerical apertureNA between 0.15 and 0.25 (e.g., 0.185 and 0.215, or 0.185 and 0.23, or0.195 and 0.25, or 0.195 and 0.225, or between 2 and 2.1). Preferablythe fiber bandwidth is greater than 2 GHz-Km, centered on a wavelengthwithin 900 nm and 1300 nm.

The core 20 extends from a centerline at r=0 to an outermost coreradius, R₁. The cladding 200 extends from the radius, R₁ to an outermostcore radius, R_(max). In some embodiments the cladding 200 of theoptical fiber 10 includes a silica based region 50 surrounding the coreand having a refractive index lower than that of silica. The silicabased cladding region 50 may comprise, for example, F and optionallyGeO₂. In some embodiments, this silica based cladding region 50 includesrandom or non-periodically distributed voids (for example filled withgas). In some embodiments the silica based region 50 extends through theentire cladding 200. In other embodiments an outer cladding layer 60surrounds the cladding region 50. In some embodiments the cladding 200of the optical fiber 10 includes a silica based region 50 surroundingthe core and having a refractive index lower than that of outer claddinglayer 60.

In some embodiments an optional silica based inner cladding layer 30 issituated between the core 20 and the down-doped region 50. In theseembodiments the cladding 200 has a relative refractive index profile,A_(CLAD)(r). An exemplary schematic relative refractive index profile ofthe optical fiber 10 is depicted in FIG. 2A. In some embodiments thedown-doped region 50 is offset from the core 20 by a width W₂=R₂−R₁, andsuch that this region begins at r=R₂ and ends at r=R₄ having a widths ofW₄=R₄−R₃ and W₅=R₄−R₂ (see, for example, FIG. 2A). In other embodimentsthe down-doped region 50 directly abuts the core 20, and may have arectangular or a trapezoidal cross sections such that this region beginsat r=R₁ and ends at r=R₄ having a widths W₄=R₄−R₃ and W₅=R₄−R₂ (see, forexample, FIG. 2B, where in this example R₂=R₁). The cladding 200 extendsfrom R₄ to an outermost cladding radius, R_(max). In some embodiments,the cladding 200 comprises Ge-P co-doped silica (for example, in layers30, and/or 60). In some embodiments, the cladding 200 comprises fluorinedoped silica, for example in layer 50. For example, in some embodimentsthe silica based region 50 (also referred as a moat herein) issurrounded, by a silica outer cladding (e.g., a pure silica claddinglayer 60), or an updoped silica based region 60. This is illustrated,for example, in FIGS. 2A and 2B. The core 20 and the cladding 200 formthe glass portion of the optical fiber 10. In some embodiments, thecladding 200 is coated with one or more coatings 210, for example withan acrylate polymer.

In the fiber embodiments with silica doped core doped with twoco-dopants the index profile can be described by the followingequation(Eq. 1)n ₁ ² r−n ₀ ²1−2₁ r ¹−2₂ r ²  Eq. 1where Δ₁ and Δ₂ are the relative (with respect to pure silica)refractive index changes due to dopants 1 and 2, respectively. For anoptimized profile, Δ₁ and Δ₂ satisfy the following conditions (Eq. 2):

$\begin{matrix}{{\alpha_{i} = {{2 - {2\frac{n_{0}}{m_{0}}\frac{\lambda}{\Delta_{i}}\frac{\mathbb{d}\Delta_{i}}{\mathbb{d}\lambda}} - {\frac{12}{5}\Delta\mspace{14mu} i}} = 1}},2} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

where Δ=Δ₁+Δ2 and n₀ is the index at the center R=0, and m₀ is thematerial dispersion at n₀.

We introduce two parameters x₁ and x₂ to describe the relative indexchanges in Eq. 3 and Eq. 4 (and Eq. 5-8) such that

$\begin{matrix}{\Delta_{1} = \frac{{\left( {\delta_{a\; 1} - \delta_{a\; 2}} \right)\left( {1 - x_{1}} \right)} + {\left( {\delta_{b\; 1} - \delta_{b\; 2}} \right)x_{2}}}{2n_{0}^{2}}} & {{Eq}.\mspace{14mu} 3} \\{\Delta_{2} = \frac{{\left( {\delta_{a\; 1} - \delta_{a\; 2}} \right)x_{1}} + {\left( {\delta_{b\; 1} - \delta_{b\; 2}} \right)\left( {1 - x_{2}} \right)}}{2n_{0}^{2}}} & {{Eq}.\mspace{14mu} 4}\end{matrix}$where⁻ _(a1) −n _(a1) ² − _(s) ²  Eq. 5⁻ _(a2) −n _(a2) ² − _(s) ²  Eq. 6⁻ _(b1) −n _(b1) ² − _(s) ²  Eq. 7⁻ _(b2) −n _(b2) ² − _(s) ²  Eq. 8where n_(a1) and n_(b1) are the refractive indices in the center of thefiber core corresponding to dopants 1 and 2 (i.e., to GeO₂ and P₂O₅; orto GeO₂ and B₂O₃, or to GeO₂ and F) respectively, n_(a2) and n_(b2) arethe refractive indices at the edge of fiber core corresponding todopants 1 and 2, respectively, n_(s) is the refractive index of puresilica, and as shown in Eq. 9n ₀ ² −n _(a1) ² n _(b1) ² n _(s) ²  Eq. 9Using the definitions above, the dopant concentration profiles can beexpressed as shown in Eq. 10 and Eq 11.C _(a) r−C _(a1) −C _(a1) −C _(a2)1−x ₁ r ⁻¹ −C _(a1) −C _(a2) x ₁ r⁻²  Eq. 10C _(b) r−C _(b) −C _(b1) −C _(b2) x ₂ r ⁻¹ −C _(b1) −C _(b2)1−x ₂ r⁻²  Eq. 11where C_(a1) and C_(b1) are the dopant concentrations in the center ofthe fiber core corresponding to dopants 1 and 2, respectively, C_(a2)and C_(b2) are the dopant concentrations at the edge of fiber corecorresponding to dopants 1 and 2, respectively and where x₁ and x₂ areparameters for the first and second dopant (e.g., GeO₂ and P₂O₅)respectively, that are weighting factors that describe the contributionsof dual dopants on the dopant concentration radial profile. The valuesfor parameters x₁ and x₂ are selected such that concentrations of thetwo dopants are always positive. Dopant concentrations can be expressedin units of mole % or can be converted to weight %.

More specifically, in the fiber embodiments with Ge-P co-doped cores,germania is disposed in the core 20 of the graded index multimodeoptical fiber 10 with a germania dopant concentration profile, C_(Ge)(r)(i.e., C_(a)(r)=C_(Ge)(r)) The core 20 has a center germaniaconcentration at the centerline, C_(a1)=C_(Ge1), greater than or equalto 0, and an outermost germania concentration, C_(G2), at R₁, whereinC_(Ge2) is greater than or equal to 0. The phosphorus (P) is disposed inthe core 20 of the graded index multimode optical fiber 10 with aphosphorus dopant concentration profile, C_(P)(r)—i.e, (i.e.,C_(b)(r)=C_(P)(r). The graded index core 20 has a center phosphorusconcentration at the centerline, C_(b1)=C_(P1), greater than or equal to0, and may have an outermost phosphorus concentration C_(P2), at R₁,wherein C_(P2) is greater than or equal to 0, depending on the profileof phosphorus concentration C_(P)(r) within the core. One exemplaryfiber profile of Ge and P dopant concentrations, C_(Ge)(r) and C_(P)(r),is shown in FIG. 2C.

The germania dopant concentration profile, C_(Ge)(r), is thus defined bythe following Eq. 12:C _(Ge)(r)=C _(Ge1)−(C _(Ge1) −C _(Ge2))(1−x ₁)r^(α1)−(C _(Ge1) −C_(Ge2))x ₁ r ^(α2)  Eq. 12

The phosphorus dopant concentration profile, C_(P)(r), is thus definedby the following Eq. 13:C _(P)(r)=C _(P1)−(C _(P1) −C _(P2))x ₂ r ^(α1)−(C _(P1) −C _(P2))(1−x₂)r^(α2)  Eq. 13

Each of the dual dopants, germania and phosphorus, are disposed in thecore of the multimode fiber in concentrations which vary with radius andwhich are defined by two alpha parameters, α₁ and α₂ of the opticalfiber 10 are each about 2. In some embodiments, 1.90<α₁<2.25 and1.90<α₂<2.25. In some embodiments 1.90<α₁<2.10, and 1.90<α₂<2.10.

If n_(Ge1) and n_(P1) are the refractive indices in the center of thefiber core corresponding to dopants 1 and 2 (for example, Ge and P),respectively, and n_(Ge2) and n_(P2) are the refractive indices at theedge of fiber core corresponding to dopants 1 and 2 (Ge and P,respectively), n_(s) is the refractive index of pure silica, and n₀²=n_(G1) ²+n_(P1) ²−n_(s) ², then the following parameters can bedefined: δ_(Ge1)=n_(Ge1) ²−n_(s) ², δ_(Ge2)=n_(Ge2) ²−n_(s) ²,δ_(P1)=n_(P1) ²−n_(s) ², δ_(P2)=n_(P2) ²−n_(s) ², and as shown in Eq. 14and Eq. 15:Δ₁=[(δ_(Ge1)−δ_(Ge2))(1−x ₁)+(δ_(P1)−δ_(P2))x ₂]/2n ₀ ²  Eq. 14andΔ₂=[(δ_(Ge1)−δ_(Ge2))x ₁+(δ_(P1)−δ_(P2))(1−₂)]/2n ₀ ²  Eq. 15and the refractive index profile for an optical fiber core co-doped withGe and P is shown in Eq. 16:n ₁ ²(r)=n ₀ ²(1−2Δ₁ r ^(α1)−2Δ₂ r ^(α2))  Eq. 16

The dopant profile parameters, x₁ (for Ge) and x₂ (for the secondcodopant), are preferably each between −10 and +10. More preferably−3<x₁<3 and −3<x₂<3. In some embodiments −1<x₁<1 and −1<x₂<1, forexample, 0.1<x₁<1 and 0.1<x₂<1, or 0.3<x₁<0.7 and 0.3<x₂<0.7. In someembodiments (e.g., fibers with the Ge−P codoped cores), 0.4<x₁<0.6 and0.4<x₂<0.6. It is noted that in some embodiments x₁=x₂, and in someembodiments x₁ does not equal x₂. The values for parameters x₁ and x₂are chosen such that GeO₂ and for the second co-dopant concentrationsare always positive.

In some embodiments, phosphorus is present at R₁ and germania is not,i.e. C_(P2) is greater than 0 and C_(G2) is equal to 0. In theseembodiments, the cladding 200 comprises fluorine to match the refractiveindex of the core at r=R₁.

In some embodiments, both germania and phosphorus are present at R₁,i.e. C_(P2) is greater than 0 and C_(Ge2) is greater than 0. In theseembodiments, the cladding 200 may either comprise fluorine to match therefractive index of the core at r=R₁, or the cladding 200 may comprisefluorine and Ge in embodiments with sufficient index-increasing germaniaat R₁ to offset the index decrease due to the fluorine at R₁.

Preferably, C_(Ge)(r) decreases with increasing radius from r=0 to r=R₁,and C_(P)(r) also decreases with increasing radius from r=0 to r=R₁.More preferably, C_(Ge)(r) monotonically decreases with increasingradius from r=0 to r=R₁, and C_(P)(r) also monotonically decreases withincreasing radius from r=0 to r=R₁. Even more preferably, C_(Ge)(r)decreases with increasing radius from r=0 to r=R₁, and C_(P1) isnonzero, and C_(P)(r) also decreases with increasing radius from r=0 tor=R₁, and C_(P1) is non zero. Still more preferably, C_(Ge)(r)monotonically decreases with increasing radius from r=0 to r=R₁, andC_(Ge1) is nonzero, and C_(P)(r) monotonically decreases with increasingradius from r=0 to r=R₁, and at least one of C_(Ge2) and C_(P2)=0. Insome embodiments both of C_(Ge2) and C_(P2) are zero.

In one group of embodiments, the germania concentration anywhere in thecore 20 is no more than 12 mole % germania, and preferably not more than11 mole % (i.e., C_(G)(r)≦11 mole %), and most preferably not more than10 mole %. For example, 0.5 mole %<C_(GeMAX)≦11 mole %, or 1 mole%<C_(GeMAX)<10 mole %. In these embodiments the P₂O₅ concentrationanywhere in the core (for all values of r from r=0 to r=R₁) is 0 to 12mole % and the maximum concentration of P₂O₅ preferably greater that 0.5mole. Preferably, the maximum concentration of P₂O₅ is less than 10 mole%. Preferably, 1 mole %<C_(GeMAX)≦11 mole % (e.g., 1 mole %<C_(GeMAX)≦10mole % and 1 mole %<C_(PMAX)<8 mole %), and/or 1 mole %<C_(PMAX)≦10 mole%). Preferably, 5 mole %<(C_(GeMAX)+C_(PMAX))≦19 mole %, more preferably5 mole %<(C_(GeMAX)+C_(PMAX))≦15 mole %. For example, when x₁=x₂=0.5, 8mole %<(C_(GeMAX)+C_(PMAX))≦10 mole %). These parameters enable opticalfibers with high bandwidth (e.g., >2 GHz-Km at 850 nm and >1 GHz-Km at980 and/or 1060 nm, and have NA compatible with VCSEL technology and ITUstandards (0.185≦NA≦0.215).

According to some embodiments, maximum P₂O₅ concentration anywhere inthe core (for all values of r from r=0 to r=R₁) is 10 to 1 mole %, insome embodiments, preferably 9 to 0 mole %; and the maximum P₂O₅concentration varies from 0.5 to 9 mole %, for example 3 to 9 mole %, or5 to 9 mole %, or between 6.5 and 8 mole %. In some embodiments, thegermania concentration the core 20, in mole %, varies between (for allvalues of r from r=0 to r=R₁) 10 and 0 mole %, and in other embodiments,between 6 and 0 mole %, and the maximum Germania concentration is,between 0.5 and 10 mole %, and in still other embodiments, between 1 and9 mole %. In some embodiments, the P₂O₅ concentration in the core 20, inmole %, varies between 9 and 0 and in other embodiments, between 8 and1, and in other embodiments, between 10 and 0.5 mole %.

More specifically, the core 20 comprises silica that is co-doped, withgermania and phosphorus sufficient to provide a graded-index refractiveindex profile. Each of the dual dopants, germania and phosphorus, aredisposed in the core of the multimode fiber in concentrations which varywith radius and which are defined by two alpha parameters, α1 and α2.That is, the germania dopant concentration varies with radius as afunction of the alpha parameters, α1 and α2, as does the phosphorusdopant concentration. The dual dopant concentrations disclosed hereinalso reduce the sensitivity with wavelength of the overall α shape ofthe refractive index of the optical fiber, which can help increase theproductivity yield of such fibers during their manufacture, therebyreducing waste and costs. As used herein, the term graded index refersto a multimode optical fiber with a refractive index having an overall αof about 2.

In some exemplary embodiments the graded index multimode fiber 10includes: (i) a silica based core 20 co-doped with GeO₂, a maximumconcentration of P₂O₅ about 1 to 10 mole %, and about 200 to 2000 ppm bywt. Cl, and less than 1 mole % of other index modifying dopants; thecore 20 having a dual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4at least one wavelength in the wavelength range between 840 and 1100 nm(preferably at 850 nm); and (ii) a silica based cladding 200 surroundingthe core 20 and comprising F and optionally GeO₂ and having at least oneregion (e.g., 50) with the refractive index lower than that of silica.At least some of these embodiments of fiber 10 have a numerical aperturebetween 0.185 and 0.215.

In some exemplary embodiments the graded index multimode fiber 10includes: (i) a silica based core 20 co-doped with GeO₂, a maximumconcentration of B₂O₃ about 1 to 10 mole %, and about 200 to 2000 ppm bywt. Cl, and less than 1 mole % of other index modifying dopants; thecore 20 having a dual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4at least one wavelength in the wavelength range between 840 and 1100 nm(preferably at 850 nm); and (ii) a silica based cladding 200 surroundingthe core 20 and comprising F and optionally GeO₂ and having at least oneregion (e.g., 50) with the refractive index lower than that of silica.At least some of these embodiments of fiber 10 have a numerical aperturebetween 0.185 and 0.225.

In some exemplary embodiments the graded index multimode fiber 10includes: (i) a silica based core 20 co-doped with GeO₂, a maximumconcentration of B₂O₃ about 1 to 10 mole %, and about 200 to 2000 ppm bywt. Cl, and less than 1 mole % of other index modifying dopants; thecore 20 having a dual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4at least one wavelength in the wavelength range between 840 and 1100 nm(preferably at 850 nm); and (ii) a silica based cladding 200 surroundingthe core 20 and comprising F and optionally GeO₂ and having at least oneregion (e.g., 50) with the refractive index lower than that of silica,and/or lower than that of cladding region 60. At least some of theseembodiments of fiber 10 have a numerical aperture between 0.185 and0.225

In some exemplary embodiments the graded index multimode fiber 10includes: (i) a silica based core 20 co-doped with GeO₂, a maximumconcentration of F about 1 to 10 mole %, and about 200 to 2000 ppm bywt. Cl, and less than 1 mole % of other index modifying dopants; thecore 20 having a dual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4at least one wavelength in the wavelength range between 840 and 1100 nm(preferably at 850 nm); and (ii) a silica based cladding 200 surroundingthe core 20 and comprising F and optionally GeO₂ and having at least oneregion (e.g., 50) with the refractive index lower than that of silica.At least some of these embodiments of fiber 10 have a numerical aperturebetween 0.185 and 0.215

According to some embodiments the bandwidth (BW) of fiber 10 is greaterthan 750 MHz-Km, more preferably, greater than 2 GHz-Km, even morepreferably greater than 4 GHz-Km, and in some embodiments greater than 7GHz-Km at about 850 nm. According to some embodiments the bandwidth offiber 10 is greater than 1500 MHz-Km, more preferably, greater than 2GHz-Km, even more preferably greater than 4 GHz-Km, and in someembodiments greater than 7 GHz-Km at about 980 nm and/or 1060 nm.According to some embodiments the bandwidth of fiber 10 is greater than1500 MHz-Km, more preferably greater than 2 GHz-Km, at about 1300 nm. Insome embodiments the bandwidth (BW) of fiber 10 is greater than 750MHz-Km, more preferably greater than 2 GHz-Km, even preferably greaterthan 4 GHz-Km, and in some embodiments greater than 7 GHz-Km at about850 nm and the BW is greater than 1500 MHz-Km, more preferred, greaterthan 2 GHz-Km at 980 nm. In some embodiments the bandwidth (BW) of fiber10 is greater than 750 MHz-Km, more preferred, greater than 2 GHz-Km,even more preferred greater than 4 GHz-Km, and in some embodimentsgreater than 7 GHz-Km at about 850 nm and the BW is greater than 1500MHz-Km, more preferred, greater than 2 GHz-Km at 1060 nm.

Preferably optical fiber 10 has restricted launch bend loss (macrobendloss) at λ=850 nm is less than 1.5 dB/turn on a 10 mm diameter mandrel,and according to some embodiments the bend loss at λ=850 nm is less than0.25 dB/turn on a 10 mm diameter mandrel.

In some embodiments the low index cladding region 50 includes F and Ge,where the volume average Ge concentration in the moat region is at least0.5 wt %. Preferably the core 20 is separated (off-set) by at least 0.5μm from the cladding region 50. Alternatively, this cladding region mayinclude random or non-periodically distributed voids (for example filledwith gas). Preferably the volume V of cladding region 50 (moat) isgreater than 30 square microns-percent (μm²-%), and more preferablygreater than 100 and less than 300 square microns-percent.

According to some embodiments the graded index multimode fiber 10comprises: (i) a silica based core 20 co-doped with GeO₂ ((preferablythe maximum amount of GeO₂ in the core is 0.5 to 9 mole %, and morepreferably 4-9 mole %) and about 0.5 to 11 mole. % (max amount P₂O₅, andless than 1 wt. % of other index modifying dopants; the core having adual alpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4 at least onewavelength in the wavelength range between 840 and 1100 nm, preferablyat 850 nm and a core diameter and a physical core diameter, (D_(C)=2R₁),wherein 45 μm≦Dc≦55 μm (and in some embodiments 47≦Dc≦53 μm); and (ii) asilica based region (cladding 200) surrounding the core 20 andcomprising F and optionally GeO₂ .

The silica based cladding region (cladding layer 50) has a refractiveindex lower than that of silica. The fiber 10 has a numerical aperturebetween 0.185 and 0.215; a bandwidth greater than 2 GHz-Km, and leastone peak wavelength λp situated in a range of 800 nm and 900 nm.According to some embodiments the multimode fiber provides a bandwidthcharacterized by λp₁ situated in a range 800 nm and 900 nm and λp₂situated in a range of 950 to 1080 nm.

According to some embodiments graded index multimode fiber comprises:(i) a silica based core region 20 co-doped with (a) GeO₂ and (b) about 1to 9 mole % P₂O₅; and about 200 to 2000 ppm by wt. Cl, and less than 1wt. % of other index modifying dopants; the core having an alpha between1.95 and 2.25 (e.g., between 2 and 2.25, or between 2.05 and 2.2) at thewavelength range between 840 nm and 1100 nm; and (ii) a silica basedregion 50 surrounding the core region comprising F and optionally GeO₂and having a refractive index lower than that of silica, wherein thefiber has a numerical aperture between 0.185 and 0.25.

The graded index multimode fiber 10 preferably has moat volume (i.e.,the volume, V, of low refractive index region 50) that is greater than40 and less than 300 square microns-percent, and a macrobend loss of at850 nm of less than 0.3 dB/turn on a 10 mm diameter mandrel. Accordingto some embodiments the moat volume, V, is greater than 100 and lessthan 300 square microns-percent, and the fiber exhibits a macrobend lossat λ=850 nm of less than 0.25 dB/turn on a 10 mm diameter mandrel.Preferably, the fiber 10 has (i) a silica based core region co-dopedwith 1-10 mole % (max) GeO₂ and about 1 to 8 mole % (max) P₂O₅, and lessthan 1 wt. % of other index modifying dopants; the core having a dualalpha, α₁ and α₂, where 1.8≦α₁≦2.4 and 1.9≦α₂≦2.4 at least onewavelength in the wavelength range between 840 and 1100 nm, preferablyat 850 nm and a physical core diameter, Dc, wherein 45≦Dc≦55 microns;and has a numerical aperture between 0.185 and 0.215; a bandwidthgreater than 2 GHz-Km, and least one peak wavelength λp situated in arange of 800 and 900 nm. In some embodiments the optical fiber 10 isstructured to provide a bandwidth characterized by the first peakwavelength λp₁ situated in a range 800 nm and 900 nm and a second peakwavelength λp₂ situated in a range of 950 nm to 1600 nm. In someembodiments the fiber core 20 further comprises about 200 to 2000 ppm bywt. Cl. Preferably, the fiber core has X mole % (max) of GeO₂ and Y mole% (max) of P₂O₅; and X>Y. In some embodiments 1≦X/Y≦8. In someembodiments the maximum concentration of GeO₂ and P₂O₅ is at the centerof the core 20, or (in the case of a fiber with a core profile that hasa centerline dip, in the core region directly adjacent to andsurrounding the centerline dip). Preferably, core 20 comprises GeO₂ andabout 1 to 11 (and more preferably 1 to 9) mole % (max) P₂O₅, such thatthe sum of GeO₂ and P₂O₅ is not more than 19 mole % and wherein thebandwidth is >750 MHz-Km at about 850 nm. Preferably, the restrictedlaunch bend loss at λ=850 nm is less than 0.25 dB/turn when measuredwhen fiber is bent at diameter of 10 mm.

According to some embodiments the multimode fiber comprises: (i) asilica based core co-doped with GeO₂ and about 0.5 to 10 mole % P₂O₅(and preferably 1 to 8 mole %), and less than 1 wt. % of other indexmodifying dopants; the core having a dual alpha, α₁ and α₂, where1.8≦α₁≦2.4 and 1.9≦α₂≦2.4 at least one wavelength in the wavelengthrange between 840 and 1100 nm, (preferably at 850 nm) and a physicalcore diameter, Dc where Dc=2R₁ and wherein 25≦Dc≦55 microns, and in someembodiments 25≦Dc≦45 microns; and (ii) a silica based cladding regionthat (a) surrounds the core and comprises F and optionally GeO₂ and (b)has a refractive index lower than that of silica. The fiber 10 has anumerical aperture between 0.185 and 0.215; a bandwidth greater than 2GHz-Km at least one wavelength situated in a range of 800 and 900 nm.

All examples shown herein are modeled.

Comparative Examples

FIG. 3 schematically depicts the germania dopant concentration profilein the core of a comparative multimode fiber with a graded indexrefractive index profile intended for operation at 0.85 μm. The core ofthis fiber is doped only with Ge—i.e., it does not include phosphorus orfluorine. FIG. 4 shows the root mean square (RMS) pulse broadening as afunction of wavelength for the fiber of FIG. 3. The pulse width reachesa minimum at the wavelength of 0.85 μm. For wavelengths away from 0.85μm, the pulse width increases very rapidly, i.e. the bandwidthdecreases. The RMS pulse broadening is less than 0.02 ns/km for allwavelengths between about 0.84 μm and about 0.86 μm, i.e., over awavelength window width of about 0.02 μm, and over a wavelength windowwidth of 0.02 μm centered at 0.85 μm. The ratio of RMS pulse broadeningat 850 nm to that at 980 nm is about 0.16 and the ratio of RMS pulsebroadening at 850 nm to that at 1300 nm is about 0.06. Thus, while thepulse broadening may be very low at one wavelength (e.g., 850 nm) inrapidly rises when operating the same optical fiber is used at adifferent wavelength (e.g., longer wavelength, such as 980 or 1300 nm).As described herein, RMS pulse broadening is the result of RMS timedelay in a multimode fiber.

Tables 1A, 2A, 3A and 4A depict parameters of two comparative fiberexamples. The two comparative examples have similar cores, butcomparative example 1 has a cladding that does not include a down dopedregion (i.e., no moat) and the comparative example 2 fiber has acladding that does includes a down doped region (i.e., it has moat). Thecores of theses comparative fiber examples include germania, but do notinclude phosphorus.

TABLE 1A 2nd dopant GeO₂ GeO₂ Concentration 2nd dopant ConcentrationConcentration (core center) (core edge) (mole %), (mole %), (mole %),(mole %), Moat Example C_(Ge1) C_(Ge2) x₁ C_(sd1) C_(sd2) x₂ (y/n)Comparative 9.44 0 0.5 0 0 0.5 n Ex. 1 Comparative 9.44 0 0.5 0 0 0.5 yEx. 2

TABLE 2A R₂, R₁, R₃, R_(max), Delta- alpha₁ alpha₂ μm μm R₄, μm μm 3Min,% Comparative 2.065 not 25 25 25 62.5 0 Ex 1 applicable Comparative2.065 not 25 26.2 29.4 62.5 −0.45 Ex2 applicableAs shown in Tables 2A and 3A, the moat value of the comparative example1 fiber is zero (no moat is present), while the moat value of thecomparative example 2 fiber is 80%-μ².Both comparative fibers exhibiting a single operating window; this wascentered about the peak wavelength, wherein λp is 849 nm and 850 nm forthe first and the comparative example, respectively. Table 4A, belowprovides the RMS pulse broadening and the bandwidths (BW) at variouswavelength, for each of the two comparative fiber examples.

TABLE 3A Wavelength Wavelength Bend loss at of first of second Moat 850nm, 10 mm Optical window at window at Volume diameter Core RMS RMS (V),%- mandrel, Numerical Diameter minimum, nm minimum, nm μm² dB/turnAperture μm Comparative 849 not applicable 0 0.82 0.200 50 Ex. 1Comparative 850 not applicable 80 0.15 0.206 50.4 Ex. 2

TABLE 4A RMS pulse RMS pulse RMS pulse broadening at broadening atbroadening BW at 850 BW at 980 BW at 850 nm, 980 nm, at 1300 nm, nm,GHz- nm, GHz- 1300 nm, ns/km ns/km ns/km km km GHz-km Comparative 0.01410.0905 0.2205 13.2 2.1 0.8 Ex. 1 Comparative 0.0141 0.0905 0.2205 13.22.1 0.8 Ex. 2

First Set of Examplary Embodiments

FIG. 2C schematically depicts the core portion (normalized radius)germania and P₂O₅ dopant concentration profiles, shown as “GeO₂” and“P”, respectively, for a multimode optical fiber exemplary of the fibersdisclosed herein. In this exemplary embodiment, α1=α2=2.038, C_(Ge1)=5.9mole % germania, C_(P1)=3.31 mole % phosphorus, C_(Ge2)=0, C_(P2)=0,x₁=0.5, x₂=0.5, and R₁=25 μm (see example 5 of Tables 1B, 3B).

FIG. 5 schematically illustrates the RMS pulse width of several Ge-Pfibers similar to that of FIG. 2A at various wavelengths (see fiberexamples 12-20 of Tables 1B and 3B), as well as the RMS pulse broadening(inner most “v” shaped curve) of a comparative fiber with Germania, butno P in the core. As shown in this figure, the RMS pulse broadening issignificantly improved for all Ge-P co-doped fibers, within the 0.8 nmto 1.2 nm operating window, relative to that of the comparative examplefiber. In addition, this figure indicates that with the larger amount Pconcentration relative to the Ge concentration at the center of the core20, the fiber also has a second operating window, which shifts towardsshorter central wavelength as the amount of phosphorus at or near theedge of the core (C_(P2)) increases. For example, when C_(Ge1)=1.18 mole% and C_(P1)=7.72 mole % (fiber example 9 of Table 1B, 2B, 3B and 4B),the central wavelength of the second operating window is 1.22 μm, whilewhen C_(Ge1)=2.36 mole % and C_(P1)=6.62 mole %, the central wavelengthof the second operating window is 1.41 μm.

When C_(Ge1)=1.18 mole % and C_(P1)=7.72 mole %, the RMS pulsebroadening is less than 0.02 ns/km for all wavelengths between about0.75 μm and about 1.3 μm, i.e. over a wavelength window width of about0.55 μm, and over a wavelength window centered at about 1.05 μm. Thebandwidth of this co-doped fiber embodiment is about 13.2 GHz-Km andcomparable to a Ge only doped fiber (comparative fiber 1) at 850 nm,however the band width BW of the Ge-P co-doped fiber of this embodimentis about 10.5 and 10.6 GHz-Km at the wavelengths of 980 and 1300 nm,respectively compared to the Ge only doped fiber which has a BW of about2.1 and 0.8 GHz-Km, respectively. This demonstrates that the co-dopedfibers can have about 5-12 times as large as the bandwidth of the fiberof the comparative example fibers a larger wavelength range. The ratioof BW at 850 nm to that at 980 and 1300, respectively, for this co-dopedfiber is 1.7 and 1.4, respectively. The ratio of BW at 850 nm to that at980 and 1300, respectively, for the comparative example, Ge only dopedfiber, is 6.4 and 15.7, respectively. Thus showing the Ge-P co-dopedfibers 10 have a broader BW window than the comparative fibers with Geonly doped core.

When C_(Ge1)=2.36 mole % and C_(P1)=7.72 mole % (fiber example 8 ofTables 1B, 2B, 3B and 4B) the RMS pulse broadening is less than 0.03ns/km for all wavelengths between about 0.75 μm and about 1.65 μm, i.e.over a wavelength window width of about 0.90 μm, while for thecomparative example fiber the RMS pulse broadening of less than 0.03ns/km corresponds only to the wavelength window between about 0.82 μmand about 0.88 μm (window width of about 0.06 or 0.07 μm). For thisexemplary embodiment, RMS pulse broadening is less than 0.02 ns/km forall wavelengths between about 0.75 μm and about 0.95 μm, i.e. over awavelength window width of about 0.2 μm, centered at 0.85 μm. The RMSpulse broadening is also less than 0.02 ns/km for all wavelengthsbetween about 1.3 μm and about 0.5 μm, i.e. over a second wavelengthwindow width of about 0.2 μm. Thus, the optical fiber of this embodimentcan operate at two different operating windows, each much broader thanthat of the comparative fiber. The bandwidth of this co-doped fiberembodiment is about 13.2, 7.9 and 9.3 GHz-Km at 850, 980 and 1300 nm,respectively. The bandwidth for a Ge only doped fiber comparativeexample is about 13.2, 2.1 GHz-Km and 0.8 at a wavelength of 850 nm, 980nm and 1300 nm, respectively. Thus, the co-doped fibers can have about4-11 times as large as the bandwidth of the fiber of the comparativeexample a larger wavelength range.

FIG. 6 illustrates the change in the second window center wavelength vs.maximum P doping level (in these embodiments corresponding to C_(P1)) inmole %, for some embodiments of Ge and P co-doped fiber.

FIG. 7 shows the root mean square (RMS) pulse broadening at 1310 nmns/km vs. maximum P doping level (mole %), for some embodiments of Geand P co-doped fiber. In these embodiments C_(P) max corresponds toC_(P1). This figure illustrates that for these embodiments the preferredmaximum P dopant level is between 5 and 9 mole %.

Exemplary Embodiments 1-27

Various additional embodiments of the Ge-P co-doped fibers will befurther clarified by the following modeled exemplary embodiments 1-27(Tables 1B, 2B, 3B and 4B). Fiber embodiments 1-27 have a down-dopedregion 50 situated in cladding 200. In these exemplary embodiments downdoped region 50 (also referred to as a moat herein) is offset from thecore 20 by a distance of 1.2 μm (R2−R1=26.2 μm−50 μm=1.2 μm). In theseexemplary embodiments some of the fiber parameters are the same—i.e.,the relative refractive index of the core (relative to pure silica) is1%, the outer radius R₁ of the core 20 is 25 μm, the outer radius R₂ ofthe inner cladding layer 30 is 26.2 μm, the radius of the outer claddingR₄=26.2 μm. In the embodiments 12-38 the minimum refractive index deltaof the cladding layer 50 (moat) was −0.45. For these embodiments x₁, x₂values are 0.1≦x₁≦1 and 0.1≦x₂≦1.

In fiber embodiments 1-27 of Tables 1B, 2B, 3B and 4B the concentrationof germania C_(Ge1) and phosphorus C_(P1) (and the outer radius R₄ ofthe cladding layer 50 in were changed to observe the effect of thechanges on fiber performance. The change in the outer radius R₃ affectedthe moat volume of the cladding. The changes in layer 50, which in turnresulted in changes in macrobend performance. Table 3B indicates thatthe bend performance of the multimode fibers 10 is better for fiberswith larger the moat volume V (volume of region 50) which is defined inEq. 17 as:

$\begin{matrix}{V = {2{\int_{R\; 2}^{R\; 4}{{\Delta(r)}r\ {\mathbb{d}r}}}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

Accordingly, it is preferable that the moat value be greater than 30μm²%, more preferably greater 50 μm²%, and even more preferably greater100 μm²%, for example between 100 and 300 μm²%.

The changes in concentration of germania C_(Ge1) and phosphorus C_(P1)and the diameter of the core (R₁) affect the numerical aperture of thefiber, and also the center wavelength of the second operating window aswell as the values for RMS pulse broadening and the bandwidth BW atvarious wavelengths. It is noted that the RMS pulse broadening is muchsmaller for fiber embodiments 1-27 than that for the comparativeexamples 1 and 2, and that the bandwidths BW at 980 nm and 1300 nm arealso much larger than that of the comparative examples 1 and 2. This isshown in Tables 1B, 2B, 3B and 4B, below.

It is also noted that in other embodiments the relative refractive indexof the core is higher or lower than 1%. For example, Δ₁max may be 0.25%0.3%, 0.5%, 0.7% or 1.1%, 1.5%, 2%, or anything therebetween.

TABLE 1B GeO₂ GeO₂ P₂O₅ P₂O₅ Examplary Concentration ConcentrationConcentration Concentration Moat Embodiment (mole %), C_(Ge1) (mole %),C_(Ge2) x₁ (mole %), C_(P1) (mole %), C_(P2) x₂ (y/n) 1 8.62 0 0.5 1.1 00.5 y 2 7.08 0 0.5 2.21 0 0.5 y 3 8.62 0 0.5 1.1 0 0.5 y 4 7.08 0 0.52.21 0 0.5 y 5 5.9 0 0.5 3.31 0 0.5 y 6 4.42 0 0.5 4.41 0 0.5 y 7 3.54 00.5 5.51 0 0.5 y 8 2.36 0 0.5 6.62 0 0.5 y 9 1.18 0 0.5 7.72 0 0.5 y 108.62 0 0.5 1.1 0 0.5 y 11 7.08 0 0.5 2.21 0 0.5 y 12 5.9 0 0.5 3.31 00.5 y 13 4.42 0 0.5 4.41 0 0.5 y 14 3.54 0 0.5 5.51 0 0.5 y 15 2.36 00.5 6.62 0 0.5 y 16 1.18 0 0.5 7.72 0 0.5 y 17 8.62 0 0.5 1.1 0 0.5 y 187.08 0 0.5 2.21 0 0.5 y 19 5.9 0 0.5 3.31 0 0.5 y 20 4.42 0 0.5 4.41 00.5 y 21 3.54 0 0.5 5.51 0 0.5 y 22 2.36 0 0.5 6.62 0 0.5 y 23 1.18 00.5 7.72 0 0.5 y 24 3.54 0 0.5 5.51 0 0.5 y 25 3.54 0 0.1 5.51 0 1.0 y26 1.80 0 0.1 7.40 0 1.0 y 27 2.72 0 0.1 6.30 0 1.0 y

TABLE 2B Delta- Examplary R₂, R₃, R_(max), 3Min, Embodiment alpha₁alpha₂ R₁, μm μm R₄, μm μm %  1 2.055 2.055 25 26.2 28.2 62.5 −0.45  22.046 2.046 25 26.2 28.2 62.5 −0.45  3 2.055 2.055 25 26.2 29.4 62.5−0.45  4 2.046 2.046 25 26.2 29.4 62.5 −0.45  5 2.038 2.038 25 26.2 29.462.5 −0.45  6 2.310 2.310 25 26.2 29.4 62.5 −0.45  7 2.026 2.026 25 26.229.4 62.5 −0.45  8 2.021 2.021 25 26.2 29.4 62.5 −0.45  9 2.018 2.018 2526.2 29.4 62.5 −0.45 10 2.055 2.055 25 26.2 31.6 62.5 −0.45 11 2.0462.046 25 26.2 31.6 62.5 −0.45 12 2.038 2.038 25 26.2 31.6 62.5 −0.45 132.310 2.310 25 26.2 31.6 62.5 −0.45 14 2.026 2.026 25 26.2 31.6 62.5−0.45 15 2.021 2.021 25 26.2 31.6 62.5 −0.45 16 2.018 2.018 25 26.2 31.662.5 −0.45 17 2.055 2.055 25 26.2 33.6 62.5 −0.45 18 2.046 2.046 25 26.233.6 62.5 −0.45 19 2.038 2.038 25 26.2 33.6 62.5 −0.45 20 2.310 2.310 2526.2 33.6 62.5 −0.45 21 2.026 2.026 25 26.2 33.6 62.5 −0.45 22 2.0212.021 25 26.2 33.6 62.5 −0.45 23 2.018 2.018 25 26.2 33.6 62.5 −0.45 242.036 2.213 25 26.2 29.4 62.5 −0.45 25 2.025 2.046 25 26.2 29.4 62.5−0.45 26 2.018 2.040 25 26.2 29.4 62.5 −0.45 27 2.022 2.043 25 26.2 29.462.5 −0.45

TABLE 3B Wavelength of first Bend loss at window at Wavelength of Moat850 nm, 10 Optical RMS second window Volume mm diameter Core Examplaryminimum, at RMS (V), %- mandrel, Numerical Diameter Embodiment nmminimum, nm μm² dB/turn Aperture μm 1 850 >1700 50 0.29 0.201 51.5 2850 >1700 50 0.29 0.201 51.5 3 850 >1700 80 0.15 0.206 50.4 4 850 >170080 0.15 0.206 50.4 5 850 >1700 80 0.15 0.206 50.4 6 850 >1700 80 0.150.206 50.4 7 850 1660 80 0.15 0.206 50.4 8 850 1410 80 0.15 0.206 50.4 8850 1220 80 0.15 0.206 50.4 10 850 >1700 140 0.04 0.215 48.2 11850 >1700 140 0.04 0.215 48.2 12 850 >1700 140 0.04 0.215 48.2 13850 >1700 140 0.04 0.215 48.2 14 850 1660 140 0.04 0.215 48.2 15 8501410 140 0.04 0.215 48.2 16 850 1220 140 0.04 0.215 48.2 17 850 >1700200 0.01 0.223 45.9 18 850 >1700 200 0.01 0.223 45.9 19 850 >1700 2000.01 0.223 45.9 20 850 >1700 200 0.01 0.223 45.9 21 850 1660 200 0.010.223 45.9 22 850 1410 200 0.01 0.223 45.9 23 850 1220 200 0.01 0.22345.9 24 850 1660 80 0.15 0.206 50.4 25 850 1660 80 0.15 0.206 50.4 26850 1410 80 0.15 0.206 50.4 27 850 1220 80 0.15 0.206 50.4

TABLE 4B Exem- RMS pulse RMS pulse plary broadening broadening BW at BWat BW at Embodi- at 980 nm, at 1300 nm, 850 nm, 980 nm, 1300 nm, mentns/km ns/km GHz-km GHz-km GHz-km 1 0.0764 0.1805 13.2 2.4 1.0 2 0.06340.1428 13.2 2.9 1.3 3 0.0764 0.1805 13.2 2.4 1.0 4 0.0634 0.1428 13.22.9 1.3 5 0.0515 0.1075 13.2 3.6 1.7 6 0.0408 0.0748 13.2 4.6 2.5 70.0314 0.0450 13.2 5.9 4.1 8 0.0236 0.0201 13.2 7.9 9.3 8 0.0178 0.017613.2 10.5 10.6 10 0.0764 0.1805 13.2 2.4 1.0 11 0.0634 0.1428 13.2 2.91.3 12 0.0515 0.1075 13.2 3.6 1.7 13 0.0408 0.0748 13.2 4.6 2.5 140.0314 0.0450 13.2 5.9 4.1 15 0.0236 0.0201 13.2 7.9 9.3 16 0.01780.0176 13.2 10.5 10.6 17 0.0764 0.1805 13.2 2.4 1.0 18 0.0634 0.142813.2 2.9 1.3 19 0.0515 0.1075 13.2 3.6 1.7 20 0.0408 0.0748 13.2 4.6 2.521 0.0314 0.0450 13.2 5.9 4.1 22 0.0236 0.0201 13.2 7.9 9.3 23 0.01780.0176 13.2 10.5 10.6 24 0.0314 0.0450 13.2 5.9 4.1 25 0.0314 0.045013.2 5.9 4.1 26 0.0213 0.0147 13.2 8.8 12.7 27 0.0209 0.0162 13.2 8.911.5The moat 50, or the entire cladding 200 (if no moat layer is present)can comprise of silica doped with fluorine, or alternatively, can beconstructed by co-doping germania and F, or phosphorus and F, such thateffective index of the co-doped region is Δ_(3Min). Preferably,−0.2<Δ_(3Min)<−0.7, for example −0.3<Δ_(3Min)<−0.5. The Ge-F or P-Fco-doping better match the viscosity of the core 20 and the cladding200. The amount of germania and fluorine or P and F in the cladding isestablished based on the amount of germania and phosphorus in the coreand their influence on the core viscosity.

Second Set of Examplary Embodiments

Various additional embodiments of the Ge-B co-doped fibers will befurther clarified by the following modeled exemplary embodiments 28-51(Tables 1C, 2C, 3C and 4C).

More specifically, in the fiber embodiments with Ge-B co-doped cores,germania is disposed in the core 20 of the graded index multimodeoptical fiber 10 with a germania dopant concentration profile, C_(Ge)(r)(i.e., C_(a)(r)=C_(Ge)(r)). The core 20 has a center germaniaconcentration at the centerline, C_(a1)=C_(Ge1), greater than or equalto 0, and an outermost germania concentration, C_(G2), at R₁, whereinC_(Ge2) is greater than or equal to 0. The boron (B₂O₃) is disposed inthe core 20 of the graded index multimode optical fiber 10 with a borondopant concentration profile, C_(B)(r)—i.e., (i.e., C_(c-d)(r)=C_(B)(r).The graded index core 20 has a center boron concentration at thecenterline, C_(c-d1)=C_(B1), greater than or equal to 0, and may have anoutermost boron concentration C_(B2), at R₁, wherein C_(B2) is greaterthan or equal to 0, depending on the profile of boron concentrationC_(B)(r) within the core. In some embodiments, germania is present atthe centerline and boron is not, i.e. C_(G1) is greater than 0 andC_(B1) is equal to 0. In some embodiments, boron is present at R₁ andgermania is not, i.e. C_(B2) is greater than 0 and C_(G2) is equal to 0.

Preferably, C_(Ge)(r) decreases with increasing radius from r=0 to r=R₁,and C_(B)(r) increases with increasing radius from r=0 to r=R₁. Morepreferably, C_(Ge)(r) monotonically decreases with increasing radiusfrom r=0 to r=R₁, and C_(B)(r) monotonically increases with increasingradius from r=0 to r=R₁. Still more preferably, C_(Ge)(r) monotonicallydecreases with increasing radius from r=0 to r=R₁, and C_(Ge1) isnonzero, and C_(B)(r) monotonically increases with increasing radiusfrom r=0 to r=R₁, and at least one of C_(B2) is non zero.

Fiber embodiments 28-51 have a down-doped region 50 situated in cladding200. Region 50 surrounds the core and has a refractive index lower thanthat of outer cladding layer 60.

In these exemplary embodiments some of the fiber parameters are thesame, i.e., the relative refractive index of the core (relative to puresilica) is 1%, the outer radius R₁ of the core 20 is 25 μm, the outerradius R₂ of the inner cladding layer 30 is 26.2 μm, the radius of theouter cladding R₄=26.2 μm. In the embodiments 12-38 the minimumrefractive index delta of the cladding layer 50 (moat) was −0.45. Forthese embodiments x₁, x₂ values are 0.1≦x₁≦1 and 0.1≦x₂≦1.

In fiber embodiments 1-27 of Tables 1C, 2C, 3C and 4C the concentrationof germania C_(Ge1) and boron C_(B1) in the core, (and the outer radiusR₄ of the cladding layer 50) were changed to observe the effect of thechanges on fiber performance. The change in the outer radius R₃ affectedthe moat volume of the cladding. The changes in layer 50 (in the moat),in turn resulted in changes in macrobend performance. It is noted thatin these embodiments the moat is off-set or separated from the core.Table 3C indicates that the bend performance of the multimode fibers 10is better for fibers with larger the moat volume V (volume of region 50)which is defined in Eq. 17.

Accordingly, it is preferable that the moat value be greater than 30μm²%, more preferably greater 50 μm²%, and even more preferably greater100 μm²%, for example between 100 and 300 μm²%.

The changes in concentration of germania C_(Ge1) and boron (B₂O₃),C_(B1) and the diameter of the core (R₁) affect the numerical apertureof the fiber, and also the center wavelength of the second operatingwindow as well as the values for RMS pulse broadening and the bandwidthBW at various wavelengths. It is noted that the RMS pulse broadening ismuch smaller for fiber embodiments 28-51 than that for the comparativeexamples 1 and 2, and that the bandwidths BW at 980 nm and 1300 nm arealso much larger than that of the comparative examples 1 and 2. This isshown in Tables 1C, 2C, 3C and 4C, below.

It is also noted that in other embodiments the relative refractive indexof the core is higher or lower than 1%. For example, Δ₁max may be 0.25%0.3%, 0.5%, 0.7% or 1.1%, 1.5%, 2%, or anything therebetween.

TABLE 1C GeO₂ GeO₂ B₂O₃ B₂O₃ Examplary Concentration ConcentrationConcentration Concentration Moat Embodiment (mole %), C_(Ge1) (mole %),C_(Ge2) x₁ (mole %), C_(B1) (mole %), C_(B2) x₂ (y/n) 28 8.69 0 0.5 02.0 0.5 y 29 7.15 0 0.5 0 8.0 0.5 y 30 8.07 0 0.5 0 4.0 0.5 y 31 7.80 00.5 0 5.0 0.5 y 32 7.55 0 0.5 0 6.0 0.5 y 33 7.55 0 10 0 6.0 0.5 y 348.69 0 0.5 0 2.0 0.5 y 35 7.15 0 0.5 0 8.0 0.5 y 36 8.07 0 0.5 0 4.0 0.5y 37 7.80 0 0.5 0 5.0 0.5 y 38 7.55 0 0.5 0 6.0 0.5 y 39 7.55 0 10 0 6.00.5 y 40 8.69 0 0.5 0 2.0 0.5 y 41 7.15 0 0.5 0 8.0 0.5 y 42 8.07 0 0.50 4.0 0.5 y 43 7.80 0 0.5 0 5.0 0.5 y 44 7.55 0 0.5 0 6.0 0.5 y 45 7.550 10 0 6.0 0.5 y 46 8.69 0 0.5 0 2.0 0.5 y 47 7.15 0 0.5 0 8.0 0.5 y 488.07 0 0.5 0 4.0 0.5 y 49 7.80 0 0.5 0 5.0 0.5 y 50 7.55 0 0.5 0 6.0 0.5y 51 7.55 0 10 0 6.0 0.5 y 52 8.69 0 0.5 0 2.0 0.5 y 53 7.15 0 0.5 0 8.00.5 y 54 8.07 0 0.5 0 4.0 0.5 y 55 7.80 0 0.5 0 5.0 0.5 y 56 7.55 0 0.50 6.0 0.5 y 57 7.55 0 10 0 6.0 0.5 y

TABLE 2C Delta- Exemplary R₂, R₃, R_(max), 3Min, Embodiment alpha₁alpha₂ R₁, μm μm R₄, μm μm % 28 1.996 1.996 25 26.2 28.2 62.5 −0.45 291.879 1.879 25 26.2 28.2 62.5 −0.45 30 1.941 1.941 25 26.2 28.2 62.5−0.45 31 1.919 1.919 25 26.2 28.2 62.5 −0.45 32 1.901 1.901 25 26.2 28.262.5 −0.45 33 2.070 2.049 25 26.2 28.2 62.5 −0.45 34 1.996 1.996 25 26.229.4 62.5 −0.45 35 1.879 1.879 25 26.2 29.4 62.5 −0.45 36 1.941 1.941 2526.2 29.4 62.5 −0.45 37 1.919 1.919 25 26.2 29.4 62.5 −0.45 38 1.9011.901 25 26.2 29.4 62.5 −0.45 39 2.070 2.049 25 26.2 29.4 62.5 −0.45 401.996 1.996 25 26.2 31.6 62.5 −0.45 41 1.879 1.879 25 26.2 31.6 62.5−0.45 42 1.941 1.941 25 26.2 31.6 62.5 −0.45 43 1.919 1.919 25 26.2 31.662.5 −0.45 44 1.901 1.901 25 26.2 31.6 62.5 −0.45 45 2.070 2.049 25 26.231.6 62.5 −0.45 46 1.996 1.996 25 26.2 33.6 62.5 −0.45 47 1.879 1.879 2526.2 33.6 62.5 −0.45 48 1.941 1.941 25 26.2 33.6 62.5 −0.45 49 1.9191.919 25 26.2 33.6 62.5 −0.45 50 1.901 1.901 25 26.2 33.6 62.5 −0.45 512.070 2.049 25 26.2 33.6 62.5 −0.45 Note, in these embodiments R₂ = R₃

TABLE 3C Wavelength Bend loss of first Wavelength at 850 nm, window atof second 10 mm Optical RMS window at Moat diameter Core Examplaryminimum, RMS Volume (V), mandrel, Numerical Diameter Embodiment nmminimum, nm %-μm² dB/turn Aperture μm 28 850 850 50 0.29 0.201 51.5 29850 870 50 0.29 0.201 51.5 30 850 850 50 0.29 0.201 51.5 31 850 870 500.29 0.201 51.5 32 850 870 50 0.29 0.201 51.5 33 850 880 50 0.29 0.20151.5 34 850 850 80 0.15 0.206 50.4 35 850 870 80 0.15 0.206 50.4 36 850850 80 0.15 0.206 50.4 37 850 870 80 0.15 0.206 50.4 38 850 870 80 0.150.206 50.4 39 850 880 80 0.15 0.206 50.4 40 850 850 140 0.04 0.215 48.241 850 870 140 0.04 0.215 48.2 42 850 850 140 0.04 0.215 48.2 43 850 870140 0.04 0.215 48.2 44 850 870 140 0.04 0.215 48.2 45 850 880 140 0.040.215 48.2 46 850 850 200 0.01 0.223 45.9 47 850 870 200 0.01 0.223 45.948 850 850 200 0.01 0.223 45.9 49 850 870 200 0.01 0.223 45.9 50 850 870200 0.01 0.223 45.9 51 850 880 200 0.01 0.223 45.9

TABLE 4C RMS pulse RMS pulse RMS pulse broadening broadening broadeningat BW at 850 BW at 1300 Examplary at 850 nm, at 980 nm, 1300 nm, nm,GHz- BW at 980 nm, GHz- Embodiment ns/km ns/km ns/km km nm, GHz-km km 280.0141 0.0495 0.1386 13.2 3.8 1.3 29 0.0140 0.0279 0.1678 13.3 6.7 1.130 0.0141 0.0247 0.0973 13.3 7.6 1.9 31 0.0140 0.0194 0.0944 13.3 9.62.0 32 0.0140 0.0181 0.1044 13.3 10.3 1.8 33 0.0140 0.0212 0.1183 13.38.8 1.6 34 0.0141 0.0495 0.1386 13.2 3.8 1.3 35 0.0140 0.0279 0.167813.3 6.7 1.1 36 0.0141 0.0247 0.0973 13.3 7.6 1.9 37 0.0140 0.01940.0944 13.3 9.6 2.0 38 0.0140 0.0181 0.1044 13.3 10.3 1.8 39 0.01400.0212 0.1183 13.3 8.8 1.6 40 0.0141 0.0495 0.1386 13.2 3.8 1.3 410.0140 0.0279 0.1678 13.3 6.7 1.1 42 0.0141 0.0247 0.0973 13.3 7.6 1.943 0.0140 0.0194 0.0944 13.3 9.6 2.0 44 0.0140 0.0181 0.1044 13.3 10.31.8 45 0.0140 0.0212 0.1183 13.3 8.8 1.6 46 0.0141 0.0495 0.1386 13.23.8 1.3 47 0.0140 0.0279 0.1678 13.3 6.7 1.1 48 0.0141 0.0247 0.097313.3 7.6 1.9 49 0.0140 0.0194 0.0944 13.3 9.6 2.0 50 0.0140 0.01810.1044 13.3 10.3 1.8 51 0.0140 0.0212 0.1183 13.3 8.8 1.6

Third Set of Exemplary Embodiments

Various additional embodiments of the Ge-F co-doped fibers will befurther clarified by the following modeled exemplary embodiments 52-101(Tables 1D, 2D, 3D and 4D).

More specifically, in the fiber embodiments with Ge-F co-doped cores,germania is disposed in the core 20 of the graded index multimodeoptical fiber 10 with a germania dopant concentration profile, C_(Ge)(r)(i.e., C_(a)(r)=C_(Ge)(r)). The core 20 has a center germaniaconcentration at the centerline, C_(a1)=C_(Ge1), greater than or equalto 0, and an outermost germania concentration, C_(G2), at R₁, whereinC_(Ge2) is greater than or equal to 0. The fluorine (F) is disposed inthe core 20 of the graded index multimode optical fiber 10 with afluorine dopant concentration profile, C_(F)(r)—i.e., (i.e.,C_(c-d)(r)=C_(F)(r). The graded index core 20 has a center fluorineconcentration at the centerline, C_(c-d1)=C_(F1), greater than or equalto 0, and may have an outermost fluorine concentration C_(F2), at R₁,wherein C_(F2) is greater than or equal to 0, depending on the profileof fluorine concentration C_(F)(r) within the core. In some embodiments,germania is present at the centerline and fluorine is not, i.e. C_(G1)is greater than 0 and C_(F1) is equal to 0. In some embodiments,fluorine is present at R₁ and germania is not, i.e. C_(F2) is greaterthan 0 and C_(G2) is equal to 0.

Preferably, C_(Ge)(r) decreases with increasing radius from r=0 to r=R₁,and C_(F)(r) increases with increasing radius from r=0 to r=R₁. Morepreferably, C_(Ge)(r) monotonically decreases with increasing radiusfrom r=0 to r=R₁, and C_(F)(r) monotonically increases with increasingradius from r=0 to r=R₁. Still more preferably, C_(Ge)(r) monotonicallydecreases with increasing radius from r=0 to r =R₁, and C_(Ge1) isnonzero, and C_(F)(r) monotonically increases with increasing radiusfrom r=0 to r=R₁, and at least one of C_(F2) is non zero. Fiberembodiments 52-101 have a down-doped region 50 situated in cladding 200.Region 50 surrounds the core and has a refractive index lower than thatof outer cladding layer 60.

In these exemplary embodiments some of the fiber parameters are thesame, i.e., the relative refractive index of the core (relative to puresilica) is 1%, the outer radius R₁ of the core 20 is 25 μm, the outerradius R₂ of the inner cladding layer 30 is 26.2 μm, the radius of theouter cladding R₄=26.2 μm. In the embodiments 12-38 the minimumrefractive index delta of the cladding layer 50 (moat) was −0.45. Forthese embodiments x₁, x₂ values are 0.1≦x₁≦1 and 0.1≦x ₂≦1.

In fiber embodiments 52-101 of Tables 1D, 2D, 3D and 4D theconcentration of germania C_(Ge1) and fluorine C_(F1) in the core, (andthe outer radius R₄ of the cladding layer 50) were changed to observethe effect of the changes on fiber performance. The change in the outerradius R₃ affected the moat volume of the cladding. The changes in layer50, which in turn resulted in changes in macrobend performance. Table 3Dindicates that the bend performance of the multimode fibers 10 is betterfor fibers with larger the moat volume V (volume of region 50) which isdefined in Eq. 17.

Accordingly, it is preferable that the moat value be greater than 30μm²%, more preferably greater 50 μm²%, and even more preferably greater100 μm²%, for example between 100 and 300 μm²%.

The changes in concentration of germania C_(Ge1) and fluorine (F) C_(F1)and the diameter of the core (R₁) affect the numerical aperture of thefiber, and also the center wavelength of the second operating window aswell as the values for RMS pulse broadening and the bandwidth BW atvarious wavelengths. It is noted that the RMS pulse broadening is muchsmaller for fiber embodiments 52-101 than that for the comparativeexamples 1 and 2, and that the bandwidths BW at 980 nm and 1300 nm arealso much larger than that of the comparative examples 1 and 2. This isshown in Tables 1D, 2D, 3D and 4D, below. Optical core diameter was notmodeled for examples 90-101 (note A).

It is also noted that in other embodiments the relative refractive indexof the core is higher or lower than 1%. For example, Δ₁max may be 0.25%0.3%, 0.5%, 0.7% or 1.1%, 1.5%, 2%, or anything therebetween.

TABLE 1D GeO₂ GeO₂ Fluorine Fluorine Examplary ConcentrationConcentration Concentration Concentration Moat Embodiment (mole %),C_(Ge1) (mole %), C_(Ge2) x₁ (mole %), C_(B1) (mole %), C_(B2) x₂ (y/n)52 4.5 0 −10 0 2.0 −10 y 53 4.5 0 −10 0 2.0 −6 y 54 4.5 0 −10 0 2.0 −4 y55 4.5 0 −10 0 2.0 −2 y 56 4.5 0 −10 0 2.0 0 y 57 4.5 0 −10 0 2.0 2 y 584.5 0 −10 0 2.0 4 y 59 4.5 0 −10 0 2.0 6 y 60 4.5 0 −10 0 2.0 −10 y 614.5 0 −10 0 2.0 −6 y 62 4.5 0 −10 0 2.0 −4 y 63 4.5 0 −10 0 2.0 −2 y 644.5 0 −10 0 2.0 0 y 65 4.5 0 −10 0 2.0 2 y 66 4.5 0 −10 0 2.0 4 y 67 4.50 −10 0 2.0 6 y 68 4.5 0 −10 0 2.0 8 y 69 4.5 0 −10 0 2.0 10 y 70 4.5 0−10 0 2.0 −10 y 71 4.5 0 −10 0 2.0 −6 y 72 4.5 0 −10 0 2.0 −4 y 73 4.5 0−10 0 2.0 −2 y 74 4.5 0 −10 0 2.0 0 y 75 4.5 0 −10 0 2.0 2 y 76 4.5 0−10 0 2.0 4 y 77 4.5 0 −10 0 2.0 6 y 78 4.5 0 −10 0 2.0 8 y 79 4.5 0 −100 2.0 10 y 80 4.5 0 −10 0 2.0 −10 y 81 4.5 0 −10 0 2.0 −6 y 82 4.5 0 −100 2.0 −4 y 83 4.5 0 −10 0 2.0 −2 y 84 4.5 0 −10 0 2.0 0 y 85 4.5 0 −10 02.0 2 y 86 4.5 0 −10 0 2.0 4 y 87 4.5 0 −10 0 2.0 6 y 88 4.5 0 −10 0 2.08 y 89 4.5 0 −10 0 2.0 10 y 90 8.22 0 0.5 0 0.5 0.5 y 91 6.80 0 0.5 01.0 0.5 y 92 5.58 0 0.5 0 1.5 0.5 y 93 8.22 0 0.5 0 0.5 0.5 y 94 6.80 00.5 0 1.0 0.5 y 95 5.58 0 0.5 0 1.5 0.5 y 96 8.22 0 0.5 0 0.5 0.5 y 976.80 0 0.5 0 1.0 0.5 y 98 5.58 0 0.5 0 1.5 0.5 y 99 8.22 0 0.5 0 0.5 0.5y 100 6.80 0 0.5 0 1.0 0.5 y 101 5.58 0 0.5 0 1.5 0.5 y

TABLE 2D alpha₂ Delta- Examplary alpha₁ at at 850 R₂, R₃, R_(max), 3Min,Embodiment 850 nm nm R₁, μm μm R₄, μm μm % 52 3.041 2.212 25 26.2 28.262.5 −0.45 53 1.995 1.920 25 26.2 28.2 62.5 −0.45 54 2.026 2.006 25 26.228.2 62.5 −0.45 55 2.040 2.032 25 26.2 28.2 62.5 −0.45 56 2.049 2.045 2526.2 28.2 62.5 −0.45 57 2.055 2.052 25 26.2 28.2 62.5 −0.45 58 2.0592.057 25 26.2 28.2 62.5 −0.45 59 2.061 2.061 25 26.2 28.2 62.5 −0.45 603.041 2.212 25 26.2 29.4 62.5 −0.45 61 1.995 1.920 25 26.2 29.4 62.5−0.45 62 2.026 2.006 25 26.2 29.4 62.5 −0.45 63 2.040 2.032 25 26.2 29.462.5 −0.45 64 2.049 2.045 25 26.2 29.4 62.5 −0.45 65 2.055 2.052 25 26.229.4 62.5 −0.45 66 2.059 2.057 25 26.2 29.4 62.5 −0.45 67 2.061 2.061 2526.2 29.4 62.5 −0.45 68 2.064 2.063 25 26.2 29.4 62.5 −0.45 69 2.0662.066 25 26.2 29.4 62.5 −0.45 70 3.041 2.212 25 26.2 31.6 62.5 −0.45 711.995 1.920 25 26.2 31.6 62.5 −0.45 72 2.026 2.006 25 26.2 31.6 62.5−0.45 73 2.040 2.032 25 26.2 31.6 62.5 −0.45 74 2.049 2.045 25 26.2 31.662.5 −0.45 75 2.055 2.052 25 26.2 31.6 62.5 −0.45 76 2.059 2.057 25 26.231.6 62.5 −0.45 77 2.061 2.061 25 26.2 31.6 62.5 −0.45 78 2.064 2.063 2526.2 31.6 62.5 −0.45 79 2.066 2.066 25 26.2 31.6 62.5 −0.45 80 3.0412.212 25 26.2 33.6 62.5 −0.45 81 1.995 1.920 25 26.2 33.6 62.5 −0.45 822.026 2.006 25 26.2 33.6 62.5 −0.45 83 2.040 2.032 25 26.2 33.6 62.5−0.45 84 2.049 2.045 25 26.2 33.6 62.5 −0.45 85 2.055 2.052 25 26.2 33.662.5 −0.45 86 2.059 2.057 25 26.2 33.6 62.5 −0.45 87 2.061 2.061 25 26.233.6 62.5 −0.45 88 2.064 2.063 25 26.2 33.6 62.5 −0.45 89 2.066 2.066 2526.2 33.6 62.5 −0.45 90 2.064 2.064 25 26.2 28.2 62.5 −0.45 91 2.0642.064 25 26.2 28.2 62.5 −0.45 92 2.065 2.065 25 26.2 28.2 62.5 −0.45 932.064 2.064 25 26.2 29.4 62.5 −0.45 94 2.064 2.064 25 26.2 29.4 62.5−0.45 95 2.065 2.065 25 26.2 29.4 62.5 −0.45 96 2.064 2.064 25 26.2 31.662.5 −0.45 97 2.064 2.064 25 26.2 31.6 62.5 −0.45 98 2.065 2.065 25 26.231.6 62.5 −0.45 99 2.064 2.064 25 26.2 33.6 62.5 −0.45 100 2.064 2.06425 26.2 33.6 62.5 −0.45 101 2.065 2.065 25 26.2 33.6 62.5 −0.45 In theseembodiments R₂ = R₃

TABLE 3D Wavelength Wavelength Bend loss of first of second at 850 nm,window at window at Moat 10 mm Optical RMS RMS Volume diameter CoreExamplary minimum, minimum, (V), %- mandrel, Numerical DiameterEmbodiment nm nm μm² dB/turn Aperture μm 52 850 1090 50 0.29 0.201 51.553 850 1090 50 0.29 0.201 51.5 54 850 1090 50 0.29 0.201 51.5 55 8501090 50 0.29 0.201 51.5 56 850 1090 50 0.29 0.201 51.5 57 850 1090 500.29 0.201 51.5 58 850 1090 50 0.29 0.201 51.5 59 850 1090 50 0.29 0.20151.5 60 850 1090 80 0.15 0.206 50.4 61 850 1090 80 0.15 0.206 50.4 62850 1090 80 0.15 0.206 50.4 63 850 1090 80 0.15 0.206 50.4 64 850 109080 0.15 0.206 50.4 65 850 1090 80 0.15 0.206 50.4 66 850 1090 80 0.150.206 50.4 67 850 1090 80 0.15 0.206 50.4 68 850 1090 80 0.15 0.206 50.469 850 1090 80 0.15 0.206 50.4 70 850 1090 140 0.04 0.215 48.2 71 8501090 140 0.04 0.215 48.2 72 850 1090 140 0.04 0.215 48.2 73 850 1090 1400.04 0.215 48.2 74 850 1090 140 0.04 0.215 48.2 75 850 1090 140 0.040.215 48.2 76 850 1090 140 0.04 0.215 48.2 77 850 1090 140 0.04 0.21548.2 78 850 1090 140 0.04 0.215 48.2 79 850 1090 140 0.04 0.215 48.2 80850 1090 200 0.01 0.223 45.9 81 850 1090 200 0.01 0.223 45.9 82 850 1090200 0.01 0.223 45.9 83 850 1090 200 0.01 0.223 45.9 84 850 1090 200 0.010.223 45.9 85 850 1090 200 0.01 0.223 45.9 86 850 1090 200 0.01 0.22345.9 87 850 1090 200 0.01 0.223 45.9 88 850 1090 200 0.01 0.223 45.9 89850 1090 200 0.01 0.223 45.9 90 850 >1700 50 0.29 0.2 note A 91850 >1700 50 0.29 0.2 note A 92 850 1570 50 0.29 0.2 note A 93 850 >170080 0.15 0.2 note A 94 850 >1700 80 0.15 0.2 note A 95 850 1570 80 0.150.2 note A 96 850 >1700 140 0.04 0.2 note A 97 850 >1700 140 0.04 0.2note A 98 850 1570 140 0.04 0.2 note A 99 850 >1700 200 0.01 0.2 note A100 850 >1700 200 0.01 0.2 note A 101 850 1570 200 0.01 0.2 note A NoteA: Optical core diameter was not modeled for examples 90-101.

TABLE 4D RMS pulse RMS pulse RMS pulse broadening broadening broadeningat BW at 850 BW at 980 BW at 1300 Examplary at 850 nm, at 980 nm, 1300nm, nm, GHz- nm, GHz- nm, GHz- Embodiment ns/km ns/km ns/km km km km 520.0148 0.0746 0.2348 12.6 2.5 0.8 53 0.0149 0.0231 0.0423 12.5 8.1 4.454 0.0149 0.0189 0.0447 12.5 9.9 4.2 55 0.0149 0.0181 0.0458 12.5 10.34.1 56 0.0149 0.0178 0.0462 12.5 10.5 4.0 57 0.0149 0.0177 0.0463 12.510.5 4.0 58 0.0149 0.0177 0.0464 12.5 10.6 4.0 59 0.0149 0.0176 0.046412.5 10.6 4.0 60 0.0148 0.0746 0.2348 12.6 2.5 0.8 61 0.0149 0.02310.0423 12.5 8.1 4.4 62 0.0149 0.0189 0.0447 12.5 9.9 4.2 63 0.01490.0181 0.0458 12.5 10.3 4.1 64 0.0149 0.0178 0.0462 12.5 10.5 4.0 650.0149 0.0177 0.0463 12.5 10.5 4.0 66 0.0149 0.0177 0.0464 12.5 10.6 4.067 0.0149 0.0176 0.0464 12.5 10.6 4.0 68 0.0149 0.0176 0.0465 12.5 10.64.0 69 0.0149 0.0176 0.0465 12.5 10.6 4.0 70 0.0148 0.0746 0.2348 12.62.5 0.8 71 0.0149 0.0231 0.0423 12.5 8.1 4.4 72 0.0149 0.0189 0.044712.5 9.9 4.2 73 0.0149 0.0181 0.0458 12.5 10.3 4.1 74 0.0149 0.01780.0462 12.5 10.5 4.0 75 0.0149 0.0177 0.0463 12.5 10.5 4.0 76 0.01490.0177 0.0464 12.5 10.6 4.0 77 0.0149 0.0176 0.0464 12.5 10.6 4.0 780.0149 0.0176 0.0465 12.5 10.6 4.0 79 0.0149 0.0176 0.0465 12.5 10.6 4.080 0.0148 0.0746 0.2348 12.6 2.5 0.8 81 0.0149 0.0231 0.0423 12.5 8.14.4 82 0.0149 0.0189 0.0447 12.5 9.9 4.2 83 0.0149 0.0181 0.0458 12.510.3 4.1 84 0.0149 0.0178 0.0462 12.5 10.5 4.0 85 0.0149 0.0177 0.046312.5 10.5 4.0 86 0.0149 0.0177 0.0464 12.5 10.6 4.0 87 0.0149 0.01760.0464 12.5 10.6 4.0 88 0.0149 0.0176 0.0465 12.5 10.6 4.0 89 0.01490.0176 0.0465 12.5 10.6 4.0 90 0.0141 0.0726 0.1497 13.3 2.6 1.2 910.0140 0.0508 0.0819 13.3 3.7 2.3 92 0.0138 0.0377 0.0414 13.5 4.9 4.593 0.0141 0.0726 0.1497 13.3 2.6 1.2 94 0.0140 0.0508 0.0819 13.3 3.72.3 95 0.0138 0.0377 0.0414 13.5 4.9 4.5 96 0.0141 0.0726 0.1497 13.32.6 1.2 97 0.0140 0.0508 0.0819 13.3 3.7 2.3 98 0.0138 0.0377 0.041413.5 4.9 4.5 99 0.0141 0.0726 0.1497 13.3 2.6 1.2 100 0.0140 0.05080.0819 13.3 3.7 2.3 101 0.0138 0.0377 0.0414 13.5 4.9 4.5

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention. Since modifications combinations,sub-combinations and variations of the disclosed embodimentsincorporating the spirit and substance of the invention may occur topersons skilled in the art, the invention should be construed to includeeverything within the scope of the appended claims and theirequivalents.

We claim:
 1. A graded index multimode optical fiber comprising: (a) acore comprising silica doped with germania and at least one co-dopant,c-d, the co-dopant comprising one of P₂O₅ or F or B₂O₃, the coreextending from a centerline at r=0 to an outermost core radius, r₁ andhaving a dual alpha, α₁ and α; (b) an inner cladding surrounding and incontact with the core; (c) an outer cladding surrounding and in contactwith the inner cladding, at least one region of the inner claddinghaving a lower refractive index than the outer cladding and beingoff-set from said core; and the germania is disposed in the core with agermania dopant concentration profile, C_(Ge1)(r), and the core has acenter germania concentration at the centerline, C_(Ge1), greater thanor equal to 0, and an outermost germania concentration C_(Ge2), at r₁,wherein C_(Ge2), is greater than or equal to 0; and wherein theco-dopant is disposed in the core with a co-dopant concentrationprofile, C_(c-d)(r), and the core has a center co-dopant concentrationat the centerline, C_(c-d1), greater than or equal to 0, and anoutermost co-dopant concentration C_(c-d2), at r₁, wherein C_(c-d2) isgreater than or equal to 0; andC_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;1.8<₁<2.4, 1.8<α₂<3.1; and −10<x₁<10 and −10<x₂<10.
 2. The optical fiberof claim 1 wherein the inner cladding region with the lower refractiveindex than the outer cladding that is off sett from the core includesrandom voids or comprised of silica doped with boron, fluorine, orco-doping of fluorine and germania.
 3. The optical fiber of claim 1wherein the concentration of fluorine at the centerline is essentiallyzero, and the concentration of fluorine increases with radius within thecore.
 4. The optical fiber of claim 3 wherein the concentration ofgermania at r₀ ranges from about 1 and about 11.5 mole %.
 5. The opticalfiber of claim 1 wherein the bandwidth is >750 MHz-Km at about 850 nm.6. The optical fiber of claim 1 wherein the bandwidth is >1500 MHz-Km atabout 850 nm.
 7. The optical fiber of claim 1 wherein the bandwidthis >1500 MHz-Km at about 980 nm.
 8. The optical fiber of claim 1 whereinthe bandwidth is >500 MHz-Km at about 1300 nm.
 9. The optical fiber ofclaim 1 where the restricted launch bend loss at 850 nm is less than 1.5dB/turn.
 10. The optical fiber of claim 1 where the restricted launchbend loss at 850 nm is less than 0.25 dB/turn.
 11. The optical fiber ofclaim 1 where the volume average F concentration in the core region isat least 0.25 wt %.
 12. The optical fiber of claim 2 where the volumeaverage Ge concentration in the moat region is at least 0.5 wt %. 13.The optical fiber of claim 1 where the core are separated by at least0.5 um from the portion of the inner cladding having a lower refractiveindex than the outer cladding.
 14. The optical fiber of claim 2 whereinthe inner cladding region having a lower refractive index than the outercladding comprises fluorine and the volume of fluorine is greater than30 μm²%.
 15. The optical fiber of claim 2 wherein the inner claddingregion having a lower refractive index than the outer cladding comprisesfluorine and the volume of fluorine is greater than 100 and less than300 μm²%.
 16. A graded index multimode optical fiber comprising: (a) acore comprising silica doped with germania and at least one co-dopant,c-d, the co-dopant comprising B₂O₃, the core extending from a centerlineat r=0 to an outermost core radius, r₁ and having a dual alpha, α₁ andα; (b) an inner cladding surrounding and in contact with the core; (c)an outer cladding surrounding and in contact with the inner cladding, atleast one region of the inner cladding having a lower refractive indexthan the outer cladding; and the germania is disposed in the core with agermania dopant concentration profile, C_(Ge1)(r), and the core has acenter germania concentration at the centerline, C_(Ge1), greater thanor equal to 0, and an outermost germania concentration C_(Ge2), at r₁,wherein C_(Ge2), is greater than or equal to 0; and wherein theco-dopant is disposed in the core with a co-dopant concentrationprofile, C_(c-d)(r), and the core has a center co-dopant concentrationat the centerline, C_(c-d1), greater than or equal to 0, and anoutermost co-dopant concentration C_(e-d2), at r₁, wherein C_(c-d2) isgreater than or equal to 0; andC_(Ge)(r)=C_(Ge1)−(C_(Ge1)−C_(Ge2))(1−x₁)r^(α1)−(C_(Ge1)−C_(Ge2))x₁r^(α2);C_(c-d)(r)=C_(c-d1)−(C_(c-d1)−C_(c-d2))x₂r^(α1)−(C_(c-d1)−C_(c-d2))(1−x₂)r²;1.8<₁<2.4, 1.8<α₂<3.1; and −10<x₁<10 and −10<x₂<10.
 17. The opticalfiber of claim 16 wherein the inner cladding region with the lowerrefractive index than the outer cladding includes random voids orcomprised of silica doped with boron, fluorine, or co-doping of fluorineand germania.
 18. The optical fiber of claim 1 wherein the bandwidth BWsatisfyes at least one of the following conditions: (i) BW>1500 MHz-Kmat about 850 nm; (ii) BW>1500 MHz-Km at about 980 nm; (iii) BW>500MHz-Km at about 1300 nm; or (ii)
 19. The optical fiber of claim 16wherein the concentration of germania at r₀ ranges from about 1 andabout 11.5 mole %.
 20. The optical fiber of claim 16 wherein thebandwidth is >750 MHz-Km at about 850 nm.